Answer:
x = 4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Equality Properties
- Combining Like Terms
Step-by-step explanation:
<u>Step 1: Define Equation</u>
2(6x + 4) - 6 + 2x = 3(4x + 3) + 1
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute: 12x + 8 - 6 + 2x = 12x + 9 + 1
- Combine like terms: 14x + 2 = 12x + 10
- Subtract 12x on both sides: 2x + 2 = 10
- Subtract 2 on both sides: 2x = 8
- Divide 2 on both sides: x = 4
9514 1404 393
Answer:
ΔLMN ~ ΔLFG; scale factor 7/3
Step-by-step explanation:
The ratios of side lengths, shortest to longest are ...
FG : GL : LF = 24 : 36 : 42 = 4 : 6 : 7 (reduced)
MN : NL : LM = 56 : 84 : 98 = 4 : 6 : 7 (reduced)
The side ratios are the same, so ΔLMN ~ ΔLFG. The scale factor is ...
MN/FG = 56/24 = 7/3
The factorized form of the expression ( 2x² - x - 6 ) is ( 2x + 3 )( x - 2 ).
Hence, the missing values are 3 and 2 respectively.
<h3>What is the factorized form of the expression?</h3>
Given the expression: 2x² - x - 6
First, we factor -1 out of -x
2x² - x - 6
2x² -1(x) - 6
Not that, -1 can also be written as 3-4
2x² + (3-4)x - 6
2x² + 3x - 4x - 6
Next, we group the first two terms and the last two terms and factor out the GCF
(2x² + 3x) - 4x - 6
x(2x + 3) - 2( 2x + 3)
Factor out the GFC which is ( 2x+3 )
We have; ( 2x + 3 )( x - 2 )
The factorized form of the expression ( 2x² - x - 6 ) is ( 2x + 3 )( x - 2 ).
Hence, the missing values are 3 and 2 respectively.
Learn more about factorization here: brainly.com/question/11994062
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A minimum because the function is positive. Positive quadratic functions always concave upwards (in a “bowl-like” shape), creating a curve/minimum at the bottom.
